# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2017-2018): c. 84%

# Discussiones Mathematicae Graph Theory

## RADII AND CENTERS IN ITERATED LINE DIGRAPHS

 Martin Knor Slovak Technical University, Faculty of Civil Engineering Department of Mathematics, Radlinského 11, 813 68 Bratislava, Slovakia L'udovít Niepel Comenius University, Faculty of Mathematics and Physics Mlynská dolina, 842 15 Bratislava, Slovakia

## Abstract

We show that the out-radius and the radius grow linearly, or almost" linearly, in iterated line digraphs. Further, iterated line digraphs with a prescribed out-center, or a center, are constructed. It is shown that not every line digraph is admissible as an out-center of line digraph.

Keywords: center, digraph, line digraph, radius.

1991 Mathematics Subject Classification: 05C20, 05C12.

## References

 [1] M. Aigner, On the linegraph of a directed graph, Math. Z. 102 (1967) 56-61, doi: 10.1007/BF01110285. [2] L.W. Beineke and R.J. Wilson, Selected Topics in Graph Theory (Academic Press, London, 1978). [3] F. Buckley and F. Harary, Distance in Graphs (Addison-Wesley, Reading, 1990). [4] M.A. Fiol, J.L.A. Yebra and I. Alegre, Line digraph iterations and the (d,k) digraph problem, IEEE Trans. Comput. C-33 (1984) 400-403, doi: 10.1109/TC.1984.1676455. [5] M. Knor, L'. Niepel and L'. Soltés, Centers in Iterated Line Graphs, Acta Math. Univ. Comenianae LXI, 2 (1992) 237-241. [6] M. Knor, L'. Niepel and L'. Soltés, Distances in Iterated Line Graphs, Ars Combin. (to appear).